- University of Virginia
- Physics Department
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Energy of a
Pendulum
A Physical Science Activity
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2003 Virginia SOLs
Objectives
Students will
- construct a pendulum;
- explain how a pendulum behaves;
- describe the potential and kinetic energy of a pendulum.
Motivation for
Learning
Demonstration of a Pendulum Swing
Materials
- Heavy duty string
- 1-kg mass
Procedure
- Tie a piece of heavy-duty string to a support on the ceiling
(or someplace high with clearance below). The string should be
long enough to reach from the ceiling to your waist after it is
tied.
- Tie a 1-kg mass to the end of the string, raise the mass and
let it swing back and forth. Explain to the students that this is
an example of a pendulum.
- Demonstrate that the mass will not move unless you lift it .
When you lift the mass (or any object) you are giving it energy.
This type of energy is called potential energy. The higher you
lift it the more potential energy you give it. When you release
the mass it moves down and the potential energy you gave it starts
changing into kinetic energy . There is always the same amount of
energy (neglecting friction), it just changes from potential to
kinetic. There is kinetic energy as long as there is movement of
the mass.
- Pull the mass back with the string taut, hold it to your nose
and release it. It will swing away from you but never quite return
to the original position. This takes some courage, because as you
look at the mass swinging back towards you, it appears that the
mass will hit you in the nose. Be careful not to give the mass a
push when you initially release it, or it may hit you in the nose!
Air friction robs some of the energy from the pendulum and it can
never swing back to its original height. Invite the students to
try holding the mass to their nose, releasing it and standing
still as the bob swings back toward their nose. Caution them
not to give the mass a push!
Background
Information
The gravitational potential energy of an object is related to
its mass and the vertical height to which the object is lifted. It can be expressed
by the following formula:
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G.P.E.= Weight X Height = mgh
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You can see from the formula that the greater the weight and the higher the
position of the ball, the greater the potential energy. The kinetic energy of
an object in motion is related to the mass of object (m) and its velocity (v).
This mathematical relationship is expressed as:
A simple pendulum is an example of simple harmonic motion. It
contiunes swinging back and forth. During this swinging, there is constant
exchange between potential and kinetic energy. When a pendulum is the farthest
up in its swing, it is at its maximum height which gives it maximum potential
energy. At this same point in the swing, the pendulum is motionless for a
fraction of a second because it is changing direction. Since the speed is
zero, the kinetic energy is also zero. After the pendulum changes direction
and begins swinging again, it is losing height, but gaining speed. This also
means that the pendulum is losing potential energy, but gaining kinetic energy.
When the pendulum reaches the very bottom of the swing, it is at its lowest
point and greatest speed. This means that the pendulum has zero potential
energy (with respect to its rest position) and maximum kinetic energy. This
pattern continues for the rest of the swings. Ignoring air resistance, the
total energy of the system (G.P.E. + K.E) should be the same at every position
in the swing.
This student activity is designed to have the students determine
that the greatest kinetic energy occurs at the very bottom of the swing. They
do this by having the pedulum hit a block and determine which part of the
swing causes the block to move the most. Students should understand that this
is a qualitative demonstration of energy transfer. They should not expect
to get precise data, but should be able to identify the points of high potential
and kinetic energies, and how the total energy is conserved.
Student
Activity
Where is the mass at the end of a
pendulum moving the fastest?
To print out the Student Copy only,
click
here.
Materials
- String about 1 meter long
- 1-kg mass with hook at the top
- 2-3 books
- Masking tape
- Small wooden block approximately (5cm X
5cm X 5cm)
- Metric ruler
Procedure
- Make a pendulum by tying one end of a
piece of string to a hook on a 1 kg mass. This mass is called the
pendulum bob. Hang the pendulum over the end of the edge of a desk
or table so that it just clears the floor.
- Tape the upper end of the string to the
side of the desk so that the pendulum can swing freely. Swing the
pendulum to be sure that it does not touch the floor.
- Place a block of wood under the
pendulum. The bob of the pendulum should hit the block at the
bottom of its first swing. Mark the spot where the block will be
with a piece of tape.
- Keeping the string taught, raise the
pendulum to a point 30 cm above the floor. You will need a ruler
to measure this distance from the floor to the bob. Keeping the
bob still, find the spot on the floor directly underneath the bob,
mark it, and measure the distance from the spot under the bob to
the wooden block. Enter the distance in the 1st data table
below.
- Release the bob and measure the distance
that the block moved from the tape. Enter the distance in the
table and repeat the experiment three times. You will need to find
the average distance and enter it in the 1st data table.
- Again, hold the bob 30 cm above the
floor. Move the wooden block horizontally towards the bob, so that
the bob will hit the block at about 1/2 the angle that the bob hit
the block previously (see the diagram). Place the wooden block on
top of 1 or 2 books so that the bob will still hit the block.
Measure the new distance from the wooden block to the bob and
enter it in table #2.
- Release the bob from the 30-cm height
and let it hit the block. Repeat the experiment three times and
find the average as before. Enter all measurements in table
#2.
Data Sheet
To print out the Data Sheet only,
click here.
- Table 1
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Trial
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Distance From Block to Bob
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Distance Block Moves
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1
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2
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3
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- Average Distance Block Moved
____________________________
- Table 2
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Trial
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Distance From Block to Bob
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Distance Block Moves
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1
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2
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3
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- Average Distance Block Moved
____________________________
- What happens to the block of wood when it was hit by
the pendulum bob?
- Kinetic energy is energy of motion and potential
energy is stored energy. What kind of energy did the bob
give to the block?
- Where would you place the block for the pendulum bob
to push the block the farthest?
- If the energy of the pendulum is either stored
(potential) or moving (kinetic), where in the swing does
the pendulum have the most potential energy? Explain how
you know.
- Where in the swing does the pendulum have the most
kinetic energy (speed)? Explain how you know.
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Students with special needs
Click here for information
on laboratories with students with special needs.
Assessment
To print out the Assessment only,
click here.
A roller coaster is very similar to a pendulum in terms of kinetic
and potential energy. Use the illustration below to answer the
questions.
1. __________ Which letter in the diagram represents the place
where the cars on the roller
coaster would have the most potential energy?
2. __________ Which letter represents the place where the cars
would have the most kinetic
energy?
3. __________ Which letter represents the place where the cars
would have the least kinetic
energy?
4. __________ Which letter represents the place where the energy
would be changing from
kinetic to potential energy?
5. __________ Which letter represents the place where the energy
would be changing from potential to kinetic energy?
6. __________ Where in the diagram would the cars be moving with
the greatest speed?
7. Why do you think that the first hill on the roller coaster must
be the tallest? (explain your answer in terms of kinetic and
potential energy.